The Diagonal Mapping in Bmoa-Type Spaces of Analytic Functions on the Polydisk

For any holomorphic function 𝑓 on the unit polydisk we consider its restriction to the diagonal, i.e., the function in the unit disc 𝔻 ⊂ ℂ defined by Diag 𝑓(𝑧) = 𝑓(𝑧, . . . , 𝑧) and prove that the diagonal map Diag maps the space of the polydisk onto the space of the unit disk.

Bloch spaces of holomorphic functions in the polydisk

This work is an introduction to anisotropic spaces of holomorphic functions, which haveω-weight and are generalizations of Bloch spaces to a polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. Some theorems on projection and diagonal mapping are proved. We establish a description of(Ap(ω))*(or(Hp(ω))*via the Bloch classes for all0<p≤1.